Transactions of the Korean Nuclear Society Virtual Autumn Meeting December 17-18 Spinodal decomposition in the Fe-Cr alloys: Effect of inhomogeneous elasticity and dislocation Wooseob Shin a , Jeonghwan Lee a , Kunok Chang a a Department of Nuclear Engineering, KyungHee University, Yong-in city, Korea * Corresponding author: kunok.chang@khu.ac.kr 1. Introduction α' precipitate hardening in Fe-Cr system has been a important research subject in terms of maintaining mechanical integrity of ferritic steels[1-7]. Precipitation can occur through the spinodal decomposition, and it has been reported that both mechanisms are involved in the precipitation of α'[2,3]. Effect of inhomogeneous elasticity and dislocation on Fe-Cr spinodal decomposition has been investigated[6] using the phase- field method, however the evaluation of the minimum Cr concentration at which spinodal decomposition occurs was not performed, and the quantitative microstructure analysis was also limited. In this study, we analyze effect of the dislocation on the kinetics of the spinodal decomposition, especially, the effect on the lowest nominal composition of Cr for the spinodal decomposition. Through this study, one can have more systematic understanding about α' nucleation in the presence of the dislocation. A role of the elasticity on the spinodal decomposition was analyzed by analytic approaches[8,9]. For cubic crystals, Cahn claimed that coherent elastic interaction increases the free energy, therefore, it inhibits the spinodal decomposition. On the other hand, Eshelby predicted that spinodal decomposition would be accelerated when elastic interaction was considered based on the theory of continuum elastic mechanics [9]. At first glance, it seems like a conflicting argument, Eshelby’s predictions describe the rate at which spinodal decomposition occurs, and Cahn’s theoretical study describes the thermodynamic conditions associated with spinodal decomposition. With the phase-field modeling, Li et al. verified that elasticity accelerates the spinodal decomposition which shows the consistency with the Eshelby’s prediction [6]. In this study, we investigated whether the presence of elasticity inhibits the initiation of spinodal decomposition, as Cahn suggested [8]. All simulations are performed at the temperature T = 535K [6] using the phase-field method. Phase-field method is a method that has been actively utilized and verified to simulate the α' phase precipitation in the Fe- Cr system [6,10,11] with free energy assessed by CALPHAD approach [12]. We conducted a set of simulations by utilizing the Multiphysics Object Oriented Simulation Environment (MOOSE) framework that can easily integrate kernels such as finite element method (FEM)-based phase-field, tensor mechanics for elasticity and nucleation. The Fe-Cr microstructure modeling solver that combines the semi-implicit Fourier- Spectral method with GPU acceleration has already been developed by the authors of this paper [11], in order to consider the elastic effect and nucleation process, we determined to utilize MOOSE framework that provides a proven module. From the perspective of solving only the Cahn-Hilliard equation[13], the FEM method, which consumes intensive time to construct the mesh, takes and order longer than the spectral method. However, the constructed mesh is reused in tensor mechanics module, therefore the performance gap greatly reduces when we consider the effect of the dislocation. 2. Simulation Details 2.1 Cahn-Hilliard equation The Cr concentration field will be evolved by solving the following Cahn-Hilliard equation [13,14]: ∂c(r, t) = ∇ ⋅ [(, ) ⋅ ∇ ( (, ) )] (1) F(r, t) = ∫ ([() + 1 2 (∇) 2 ]+ (, )) (2) The molar free energy F(r, t) in Eq.1 is given by Eq. 2, and M(r, t) is the mobility of the diffusion species. In this study, we assumed that mobility is a constant, and the value was set to 1.0. 2.2 Free energy of Fe-Cr system with dislocation The regular-solution type chemical free energy f(c) in Eq. 2 is obtained from [15] f(c) = (1 − ) + + (1 − ) + ( + (1 − ) ln(1 − ) (3) where c is the composition of Cr, and G 0 and G 0 are the molar Gibbs free energies for the Fe and Cr, respectively. is the interaction parameter of Fe and Cr. The detailed numbers are written in [11,15]. We set the temperature T = 535K. We determined the elastic energy density f e (, ) using Eq. 2. We implemented KHS elastic schemes [16]. The stiffness tensor and misfit strain are obtained by the interpolation and create a global stiffness tensor, () = , ×+ , × (1 − ) and the global strain is